{"paper":{"title":"Leibniz algebras associated with representations of the Diamond Lie algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"B.A. Omirov, I.A. Karimjanov, S. Uguz","submitted_at":"2015-07-06T08:10:10Z","abstract_excerpt":"In this paper we describe some Leibniz algebras whose corresponding Lie algebra is four-dimensional Diamond Lie algebra $\\mathfrak{D}$ and the ideal generated by the squares of elements (further denoted by $I$) is a right $\\mathfrak{D}$-module. Using description \\cite{Cas} of representations of algebra $\\mathfrak{D}$ in $\\mathfrak{sl}(3,{\\mathbb{C}})$ and $\\mathfrak{sp}(4,{\\mathbb{F}})$ where ${\\mathbb{F}}={\\mathbb{R}}$ or ${\\mathbb{C}}$ we obtain the classification of above mentioned Leibniz algebras. Moreover, Fock representation of Heisenberg Lie algebra was extended to the case of the alge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01349","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}